Question

If we roll a fair six-sided die three times, and let X be the number of results that are divisible by 2, what is the probability that X=2?

Answer 1

well this is a big sample space

Answer 2

yes!

Answer 3

for three die, X can equal 0 , 1 , 2, or 3 .
X = 0 means all three dice are not divisible by 2
X = 1 means 1 of the dice is divisible by 2
X = 2 means 2 of the dice are divisible by 2
X = 3 means all three dice are divisible by 2

Answer 4

riight okay gotcha

Answer 5

but we want to do 3 dice. ok so lets see

Answer 6

well we are rolling 1 dice three times

Answer 7

divisible by 2 means 'even' , so lets use even.
for X = 2 we have
(even, even , odd) or ( even , odd, even) or (odd, even , even)

Answer 8

now we count up
for (even, even, odd ) we have 3 x 3 x 3
for (even, odd, even) we have 3 x 3 x 3
for ( odd, even, even) we have 3 x 3 x 3 .
now there are a total of 6x6x6 possible ways to throw three die.
so ( 3 x 3 x 3 x 3 ) / ( 6 x 6 x 6 )

Answer 9

this is because there are 3 even numbers 2,4,6 and 3 odd numbers 1,3,5

Answer 10

okay, i see!

Answer 11

assuming i read the question correctly, it could be more clearly phrased

Answer 12

thank you for your help. i appreciate it!

Answer 13

:D

Answer 14

you can also see it as a binomial dist...3 trials...success probability 1/2

thus

\[P(X=2)= {3 \choose 2} \left(\frac{1}{2}\right)^3=\frac{3}{8}\]

Answer 15

yes that works too , that is probably easier than my approach

Answer 16

hmm, this is because each throw is independent and probability of even is 1/2

Answer 17

binomial dist is what unit i am in now. Thanks @zarkon